Question

How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 16, and 12 units in length?

Answer 1

Area of triangle is `107.32` units.

Explanation:

If three sides of a triangle are `a`, `b` and `c`, according to Heron's formula its area is given by

`sqrt(s(s-a)(s-b)(s-c))`, where `s=1/2(a+b+c)` is semi perimeer of the triangle.

In the given triangle the three sides are `15`, `16` and `12` and semi perimeter is `1/2xx(15+16+12)=1/2xx43=21.5`.

Hence area is given by

`sqrt(22.5(22.5-15)(22.5-16)(22.5-12))`

or `sqrt(22.5xx7.5xx6.5xx10.5)=sqrt11517.1875=107.32`